Geodesic
Estimation of convergence of spectral element method in CAE Fidesys based on exact solution of the Lame problem for elastoplastic materials using an automated regression testing system
Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 272-284

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This paper considers convergence estimation of the spectral element method implemented in CAE Fidesys. It was based on exact analytical solutions of the Lame problems in small deformations in the elastic and elastic-perfectly plastic obeying Huber-von Mises yield criterion formulations. Due to the symmetry, we consider quarters of the models. Numerical results were obtained in the CAE Fidesys strength analysis system using the finite element method for the first and second orders and the spectral element method for the third to ninth orders. Based on the results obtained, an analysis was carried out to determine the nature of the decrease in the errors of the CAE Fidesys spectral element method with an increase in the order of the elements. The study was conducted using a specialized automated testing system. The results of the work can be useful in making a decision on the use of the spectral element method in industrial calculations.
Keywords: automated testing system, autotests, finite element method, spectral element method, exponential convergence, CAE Fidesys, elastoplastic model, Lame problem, curvilinear boundaries. 
@article{CHEB_2022_23_4_a23,
     author = {V. A. Levin and V. V. Kozlov and E. D. Komolova and A. V. Filatova and M. A. Kartsev},
     title = {Estimation of convergence of spectral element method in {CAE} {Fidesys} based on exact solution of the {Lame} problem for elastoplastic materials using an automated regression testing system},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {272--284},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a23/}
}
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%A M. A. Kartsev
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V. A. Levin; V. V. Kozlov; E. D. Komolova; A. V. Filatova; M. A. Kartsev. Estimation of convergence of spectral element method in CAE Fidesys based on exact solution of the Lame problem for elastoplastic materials using an automated regression testing system. Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 272-284. http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a23/